While the connection is established between user's source and destination pairs, initial value number of packets in window, \( w(0) \)  is calculated by summing up the packets which are in transit as well as in queue on the resources which appear in user's route. Window size is adjusted with time and finally it converges to unique stable point \( w^* \) . Simulation is run for 15000 iteration and convergence of window size for four users are mentioned in Table REF . The value of scaling parameter, \( k \) , may be any positive number. Here, in the paper it is fixed as \( 0.1 \)  and each user's data sending amount is fixed as \( 10Mb \) . \( w(0) \)  of User \( 1-4 \)  are evaluated as \( 25.1012\mbox{ } Mb, 15.2063\mbox{ } Mb, 20.4796\mbox{ } Mb\)  and \( 35.6423 \mbox{ } Mb\) , respectively. These values are taken as input for all approaches (the proposed, La's [1]} and Mo's [2]}). In the proposed method, the value of \( w_i(t) \)  depends on the delays (\( d_{prop}^i \) , \( d_Q^i(t) \)  and \( d_{trans}^i(t) \) ), \( s_i(t) \) , willingness to pay \( p_i(t) \)  and previous window size \( w_i(t-1) \)  for user \( i \) . \( w_i(t) \)  will decrease exponentially with time and the value of \( w_i(t) \)  makes \( s_i(t) \approx 0 \) , is termed as optimal window size \( w_i^* \)  of the user \( i \) . As the window updates the equations for all the approaches are different hence, convergence rate will be different with difference in the value of \( w_i^* \) . Mo's approach gives the value of \( w^* \)  for all the users; User \( 1-4 \)  as \( 3.2378\mbox{ } Mb, 15.2946\mbox{ } Mb, 5.2962\mbox{ } Mb\)  and \( 9.9753\mbox{ } Mb\) , respectively. La's approach gives the value of \( w^* \)  of all users; User \( 1-4 \)  as \( 1.3471\mbox{ } Mb, 7.7192\mbox{ } Mb, 2.0598\mbox{ } Mb\)  and \( 2.0986\mbox{ } Mb\) , respectively. By using the proposed approach, User \( 1-4 \)  get \( w^* \)  values as \( 1.3568\mbox{ } Mb, 7.8302\mbox{ } Mb, 2.0746\mbox{ } Mb\)  and \( 2.1107\mbox{ } Mb\) , respectively. Window update equation keeps changing dynamically with the varying value of transmission delay, \( d_{trans}(t) \)  unlike, propagation delay, \( d_{prop} \)  in La's and Mo's, which was static. The proposed approach provides a unique stable value of window size, \( w^* \)  as in La's approach and is quite approximate to the value obtained through static (La's) approach. Mo's approach uses both propagation and queuing delays as static and it assumes less number of packets in queue irrespective of large number of incoming packets in the network hence, provides higher value of \( w^* \) . The proposed method provides dynamicity in the previous approaches by updating the window size based on transmission delay and gets stable value of window size, \( w^* \) .
<TABLE>